Integrable decompositions and superposed nonlinear solutions of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation

The phenomenon of shallow water waves in nature attracts the attention of scholars and plays an important role in fields such as marine ecology, tidal waves, solitary waves, and offshore engineering. To better understand the phenomenon of shallow water waves, we investigate the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (2D-CDGKS) equation from the perspective of integrable decomposition. By utilizing the Lax pairs and formal variable separation (FVS) method, the 2D-CDGKS equation can be decomposed into the Sharma-Tasso-Olver (STO) equation, the integrable Svinolupov-Sokolov (SS) equation, and the Sawada-Kotera (SK) equation etc. We construct some novel exact solutions by linear superposing the integrable decomposition relations. Additionally, the superposition of two-soliton solution with three-soliton solution, two-soliton solution propagating on periodic cnoidal background waves, and soliton-cnoidal wave interaction solutions with interesting dynamics, are explored. Our results have important significance for understanding of the physical events consolidate the complex system under consideration and offering vital insights into the intricate dynamics of its behavior. Furthermore, the present work will enrich the investigation of nonlinear dynamics in high-dimensional nonlinear system, and provide theoretical support for the related experimental phenomena.